Answer:
x = 9
Step-by-step explanation:
Consider the below figure attached with his question.
In the below figure [tex]FA=x+1, FB=x+6, GA=x-1\text{ and }GC=x+3[/tex].
According to Basic Proportionality Theorem (BPT), if a line is parallel to one side of a triangle, then it divides the two remaining sides in the same ratio.
Using BPT theorem,
[tex]\dfrac{FA}{FB}=\dfrac{GA}{GC}[/tex]
[tex]\dfrac{x+1}{x+6}=\dfrac{x-1}{x+3}[/tex]
On cross multiplication we get
[tex](x+1)(x+3)=(x-1)(x+6)[/tex]
[tex]x^2+3x+x+3=x^2+6x-x-6[/tex]
[tex]4x+3=5x-6[/tex]
[tex]4x-5x=-6-3[/tex]
[tex]-x=-9[/tex]
[tex]x=9[/tex]
Hence, FG║BC if the value of x is 9.
